FATIGUE CRACK GROWTH SIMULATIONS USING EXTENDED ISOGEOMETRIC ANALYSIS

Abstract

Scientific and technological developments stem from the pursuit towards perfection. However, in spite of all scientific developments, the materials possess flaws/defects. When subjected to mechanical load, these defects may grow and eventually the structures/components fail. The objective of fracture mechanics as a scientific discipline is to avoid or at least predict failure so that the damaging consequences of catastrophic failure can be avoided. This may finally lead to catastrophic failure of components resulting in loss of property and lives. Ensuring the safety and reliability of the engineering component/structure is of great concern to engineering community. The fracture behavior of natural and man-made structures becomes a serious issue due to the presence of defects (voids and inclusions). External loading of these structures may cause either the initiation of new cracks or propagation of an existing crack. Over the years, a range of analytical, experimental and numerical approaches has been proposed to investigate the behavior of materials in the presence of flaws. Due to the scarcity of analytical solutions and also due to the versatility of the numerical methods in handling complex practical problems, research efforts continue to focus on the existing as well as improved numerical schemes. A new class of numerical method known as XIGA has been developed over the years. This method is attractive as compared to finite element method. In isogeometric analysis (IGA), non-uniform rational B-splines (NURBS) basis functions are employed for defining the geometry as well as the solution. Use of NURBS gives smooth solutions due to their higher order continuity. In investigating the problems involving flaws (cracks, holes and inclusions), the advantage of isogeometric analysis (IGA) and extended finite element method (XFEM) are combined together. The NURBS basis functions models the geometry exactly, and the enrichment functions enrich the solution approximation function. The partition of unity (PU) enrichment of solution approximation in IGA is known as extended isogeometric Abstract ii i analysis (XIGA). In XIGA, the control points influenced by the geometric flaws are locally enriched to capture the singularities produced in the solution. According to the location of the crack, few degrees of freedom are added at the selected control points of the original IGA. This thesis work is focused on the effective implementation of XIGA for linear elastic fracture analysis of crack growth problems under mode-I loading. The effectiveness and versatility of this method has been demonstrated through the solution of various problems. A comparative study of fatigue crack growth analysis of an edge or center crack in homogeneous, bi-material, FGM and bi-layered FGM is performed under mode-I loading. The numerical results obtained by XIGA (using coarse net) and XFEM (using fine mesh) are compared with available analytical solutions, and found in good agreement with available analytical solutions. In FGM, the evaluation of derivatives of strain is required. Hence, higher order functions are required for good solutions. Use of NURBS gives smooth solutions sue to their higher order continuity. Hence, XIGA is better suited for fatigue crack growth analysis an edge or center crack in FGM and bi-layered FGM. Thus, XIGA is used further for the remaining thesis work.. Fatigue crack growth analysis of an edge or center crack in homogenous, bi-material, FGM and bi-layered FGM is performed in the presence of defects under mode-I loading. These simulations show that the effect of holes is more severe as compared to inclusions, and the presence of defects significantly reduces the fatigue life of two-dimensional plane structure. It is observed that the modeling of defects in whole domain leads to tremendous increase in CPU time. A strain energy based homogenization approach is proposed to compute the equivalent properties of the materials in the presence of defects. The multiple defects need to be modeled in a 30% region (rectangular region) of the domain near the crack tip with actual properties, and the remaining domain is modeled with equivalent properties obtained through Abstract iv homogenization. This approach is named as semi homogenized XIGA (SH-XIGA). It significantly improves the computational efficiency without compromising on the accuracy. Finally, a crack growth analysis of an edge or center crack in homogenous, equivalent composite and FGM plate is performed using XIGA and XFEM under different types of loads and boundary conditions. The mathematical formulation of plate is done using first order shear deformation theory (FSDT). The normalized moment intensity factor values for homogenous material obtained by both XIGA and XFEM are compared available literature results. The normalized moment intensity factor values obtained for cracked equivalent composite plate is compared with cracked FGM plate under same load and boundary condition. The requirement of higher order continuity in plates is easily maintained by using higher order NURBS basis functions.